Question

answer the questions below.
(a) the perimeter of a rectangular field is 358 m.
if the length of the field is 98 m, what is its width?
width of the field: m
(b) the area of a rectangular painting is 3264 \\(\mathrm{cm}^2\\).
if the width of the painting is 51 cm, what is its length?
length of the painting: cm

Explanation:

Step1: Recall rectangle perimeter formula

Perimeter $P = 2(l + w)$, where $l$ = length, $w$ = width

Step2: Substitute known values (part a)

$358 = 2(98 + w)$

Step3: Solve for width (part a)

First, divide both sides by 2: $\frac{358}{2} = 98 + w$
$179 = 98 + w$
Subtract 98: $w = 179 - 98 = 81$

Step4: Recall rectangle area formula

Area $A = l \times w$

Step5: Substitute known values (part b)

$3264 = l \times 51$

Step6: Solve for length (part b)

$l = \frac{3264}{51} = 64$

Answer:

Width of the field: 81 m
Length of the painting: 64 cm